Question

Determine if the lines are parallel perpendicular or neither x -y=4 and x+y=9

Answer 1

Answer:

The line x -y=4  is perpendicular to the line x+y=9.

Step-by-step explanation:

Here, the equation Line 1  :   x  - y = 4

and  the equation Line 2   :   x  +  y = 9

Now, in the STANDARD FORM OF LINE EQUATION:

y =  m x  + c, here m = slope of the equation.

Line  1  transforms into :   y =  x - 4

⇒ Here, slope m 1  = 1

Line  2  transforms into :   y =  -x +  9

⇒ Here, slope m 2  = -1

Any two given lines in the Cartesian Plane  are said to be perpendicular to each other if the product of their slopes is -1

Here, m1 x m2  =  (1) x (-1)  = (-1)

Hence, the line x -y=4  is perpendicular to the line x+y=9.